By differentiation with respect to \(\alpha \)  at \(\alpha =0\)  this duality invariance translates into the identity[1]}, [2]},
\(\vec{R}\cdot \frac{\partial {\cal H}_{RS}(\vec{R},\vec{R}^*)}{\partial \vec{R}} \, - \,\vec{R}^*\cdot \frac{\partial {\cal H}_{RS}(\vec{R},\vec{R}^*)}{\partial \vec{R}^*}=0,\) 
